Stochastic representation for anisotropic permeability tensor random fields

Johann Guilleminot (1) , Christian Soize (1) , R. Ghanem (2)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 USC - Department of aerospace and mechanical engineering

In this paper, we introduce a novel stochastic model for the permeability tensor associated with stationary random porous media. In the light of recent works on mesoscale modeling of permeability, we first discuss the physical interpretation of the permeability tensor randomness. Subsequently, we propose a nonparametric prior probabilistic model for non-Gaussian permeability tensor random fields, making use of the information theory and a maximum entropy procedure, and provide a physical interpretation of the model parameters. Finally, we demonstrate the capability of the considered class of random fields to generate higher levels of statistical fluctuations for selected stochastic principal permeabilities. This unique flexibility offered by the parameterization of the model opens up many new possibilities for both forward simulations (e.g. for uncertainty propagation in predictive simulations) and stochastic inverse problem solving.

Mots clés: transport properties; random media; probabilistic methods; random field; permeability tensor

Domaines: Mécanique [physics.med-ph]; Matériaux; Probabilités [math.PR]

Johann Guilleminot, Christian Soize, R. Ghanem. Stochastic representation for anisotropic permeability tensor random fields. International Journal for Numerical and Analytical Methods in Geomechanics, 2012, 36 (13), pp.1592-1608. ⟨10.1002/nag.1081⟩. ⟨hal-00724651⟩